Shinshu summer workshop on probability theory

Book

• T. Funaki, Y. Otobe and B. Xie, Stochastic Partial Diffenerial Equations (in Japanese), Iwanami Shoten, March 2019. ISBN: 9784000298254.
  
  

Refereed Papers

• T. Funaki, B. Xie, Global solvability and convergence to stationary solutions in singular quasilinear stochastic PDEs. Stoch. Partial Differ. Equ. Anal. Comput. 10 (2022), no. 3, 858--897.doi.org/10.1007/s40072-022-00243-z.
• B. Xie, Log-Harnack inequality for reflected SPDEs driven by multiplicative noises and its applications. Stoch. Partial Differ. Equ. Anal. Comput. 10 (2022), no. 2, 419--445.doi.org/10.1007/s40072-021-00203-z.
• T. Funaki, M. Hoshino, S. Sethuraman and B. Xie, Asymptotics of PDE in random environment by paracontrolled calculus, Annales de l'Institut Henri Poincaré-Probabilités et Statistiques 57 (2021), No. 3, 1702–-1735. doi.org/10.1214/20-AIHP1129.
• L. Goudenège and B. Xie, Ergodicity of stochastic Cahn-Hilliard equations with logarithmic potentials driven by degenerate or nondegenerate noises. J. Differential Equations 269 (2020), no. 9, 6988--7014. doi.org/ 10.1016/j.jde.2020.04.047.
• B. Xie, A note on random strings with values in a bounded convex domain. RIMS Kôkyûroku Bessatsu, B79 (2020), Res. Inst. Math. Sci. (RIMS), 199-213.
• M. Niu and B. Xie, Comparison theorem and decorrelation for stochastic heat equation driven by Lévy space-time white noise, Discrete & Continuous Dynamical Systems - B, 24 (2019), no. 7, 2989--3009. doi:10.3934/dcdsb.2018296.
• B. Xie, Hypercontractivity for space–time white noise driven SPDEs with reflection. J. Differential Equations 266 (2019), no. 9, 5254--5277. doi:10.1016/j.jde.2018.10.022.
• M. Niu and B. Xie, Wang's Harnack inequalities for space-time white noises driven SPDEs with two reflecting walls and their applications. J. Math. Anal. Appl. 469 (2019), no. 2, 568--593.
• B. Xie, Intermittency for stochastic partial differential equations driven by strongly inhomogeneous space-time white noises. J. Differential Equations 264 (2018), no. 2, 1050-–1079.
• B. Xie, Some effects of the noise intensity upon non-linear stochastic heat equations on $[0,1]$, Stochastic Process. Appl., 126 (2016), 1184--1205.
• T. Funaki, M. Sasada, M. Sauer and B. Xie, Fluctuations in an evolutional model of two-dimensional Young diagrams, Stochastic Process. Appl., 123 (2013), 1229--1275.
• J.-L. Wu and B. Xie, On a Burgers type nonlinear equation perturbed by a pure jump Lévy noise in $R^d$, Bull. Sci. Math., 136 (2012), 484--506.
• B. Xie, Impulsive noise driven 1-dimensional higher order fractional partial differential equations, Stochastic Analysis and Applications, 30 (2012), 122--145.
• M. Niu and B. Xie, Impacts of Gaussian noises on the blow-up times of nonlinear stochastic partial differential equations, Nonlinear Analysis: Real World Applications, 13 (2012), 1346--1352.
• B. Xie, Uniqueness of Invariant Measures of Infinite Dimensional Stochastic Differential Equations Driven by Lévy Noises, Potential Analysis, 36 (2012), 35--66.
• B. Xie, The growth estimates for direction dependent random fields, Far East J. Math. Sci. (FJMS), 44 (2010), 181--195.
• M. Niu and B. Xie, Regularity of a fractional partial differential equation driven by space-time white noise, Proc. Amer. Math. Soc., 138 (2010), 1479--1489.
• T. Funaki and B. Xie, A stochastic heat equation with the distributions of L&eactuevy processes as its invariant measures, Stochastic Process. Appl., 119 (2009), 307--326.
• B. Xie, On pathwise uniqueness of stochastic evolution equations in Hilbert spaces. J. Math. Anal. Appl. 344 (2008), no. 1, 204-–216.
• B. Xie, The moment and almost surely exponential stability of stochastic heat equations. Proc. Amer. Math. Soc. 136 (2008), no. 10, 3627--3634.
• B. Xie, Stochastic differential equations with non-Lipschitz coefficients in Hilbert spaces, Stoch. Anal. Appl., 26 (2008), 408--433.
• B. Xie, The stochastic parabolic partial differential equation with non-Lipschitz coefficients on the unbounded domain, J. Math. Anal. Appl., 339 (2008), 705--718.
• L. Lei, L.-M. Wu and B. Xie, Large Deviations and Deviation Inequality for Kernel Density Estimator in $L^1 (R^d)$-distance, Development of Modern Statistics and Related Topics, Ser. Biostat., 1 (2003), 89--97, World Sci. Publishing.
• B. Xie, Hypercontractivity of Hamilton-Jacobi equations and related inequalities, J. Math. (Wuhan), 23 (2003), 397--402.